Perpendicular Lines

Perpendicular lines are two lines that intersect at a 90-degree angle. This means that if you were to measure the angles formed by the intersection of the lines, you would find that they are each 90 degrees.

Characteristics of Perpendicular Lines:

• Perpendicular lines have slopes that are negative reciprocals of each other. If the slope of one line is m, then the slope of a line perpendicular to it is -1/m.
• When graphed on the coordinate plane, perpendicular lines form a "L" shape where they intersect.
• Perpendicular lines are commonly denoted by the symbol ⊥, which is placed between the lines to show that they are perpendicular.

Example:

Consider two lines with slopes m1 = 2 and m2 = -1/2. These slopes are negative reciprocals of each other, so the lines are perpendicular.

Study Guide:

In order to understand perpendicular lines, it's important to grasp the concept of slope and how it relates to the angle of intersection between two lines. Practice finding the slope of various lines and identifying when lines are perpendicular based on their slopes. Additionally, work on graphing perpendicular lines on the coordinate plane and identifying the 90-degree angle formed by their intersection.

Remember to also study the properties of perpendicular lines and how they relate to geometric shapes and angles. This will help reinforce your understanding of the concept.